Property-theoretic statement

Definitions used

Normal subgroup

Transfer condition

A subgroup property is said to satisfy transfer condition if whenever are subgroups of and has property in , has property in .

Related facts

Further facts

Second isomorphism theorem: This result equates the quotient of the non-normal subgroup, by the intersection, with the quotient of the product of subgroups, by the normal subgroup. Specifically, it states that if is normal in and is any subgroup of , we have .